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Journal Article

A method for determining the non-existence of a common quadratic Lyapunov function for switched linear systems based on particle swarm optimisation

Duarte-Mermoud M.A., Ordonez-Hurtado R.H., Zagalak Petr

: International Journal of Systems Science vol.43, 11 (2012), p. 2015-2029

: GAP103/12/2431, GA ČR

: Switched linear systems, Lyapunov function, particle swarm optimization

: 10.1080/00207721.2012.687787

: http://library.utia.cas.cz/separaty/2012/AS/zagalak-0382169.pdf

(eng): The existence of a common quadratic Lyapunov function (CQLF) for a switched linear system guarantees its global asymptotic stability. Even if progress in finding the conditions for the existence/non-existence of a CQLF is significant, especially in switched linear systems consisting of N second-order systems or two systems of order n, the general case of N systems of order n still remains open. In this article, a sufficient condition for the non- existence of a CQLF for N systems of order n is derived. Based on the condition, a new method for determining the non-existence of a CQLF, using particle swarm optimisation, was designed and is described. Examples illustrating the proposed method are introduced at the end of this article.

: BC